Quadratic equation for 4x²-4x+1=0 using this steps

Step1.Determine the values of a.b and c.

Step2.Substitute the values of a band c in the quadratic formula.

Step3.Solve to find the solutions.

Step4.Application of the Steps

Step5.Check by substituting each solution in the original equation

Let's solve the quadratic equation \(4x^2 - 4x + 1 = 0\) using the steps provided.

### Step 1: Determine the values of \(a\), \(b\), and \(c\).
The standard form of a quadratic equation is \(ax^2 + bx + c = 0\). Comparing this to the given equation \(4x^2 - 4x + 1 = 0\):
- \(a = 4\)
- \(b = -4\)
- \(c = 1\)

### Step 2: Substitute the values of \(a\), \(b\), and \(c\) in the quadratic formula.
The quadratic formula is:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Substitute \(a = 4\), \(b = -4\), and \(c = 1\) into the formula:
\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(4)(1)}}{2(4)}
\]
\[
x = \frac{4 \pm \sqrt{16 - 16}}{8}
\]
\[
x = \frac{4 \pm \sqrt{0}}{8}
\]

### Step 3: Solve to find the solutions.
Since \(\sqrt{0} = 0\), the equation simplifies to:
\[
x = \frac{4 \pm 0}{8}
\]
This gives only one solution:
\[
x = \frac{4}{8} = \frac{1}{2}
\]

Thus, the solution to the quadratic equation is \(x = \frac{1}{2}\).

### Step 4: Application of the Steps
After applying the quadratic formula, we found that the only solution is \(x = \frac{1}{2}\).

### Step 5: Check by substituting the solution in the original equation.
Now, let's substitute \(x = \frac{1}{2}\) into the original equation \(4x^2 - 4x + 1 = 0\):

\[
4\left(\frac{1}{2}\right)^2 - 4\left(\frac{1}{2}\right) + 1 = 0
\]
\[
4 \times \frac{1}{4} - 4 \times \frac{1}{2} + 1 = 0
\]
\[
1 - 2 + 1 = 0
\]
\[
0 = 0
\]
The solution checks out, as the left side equals the right side.

### Conclusion:
The solution to the equation \(4x^2 - 4x + 1 = 0\) is \(x = \frac{1}{2}\).

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Would you like more details or have any questions?

Here are 5 related questions:
1. What happens if the discriminant \(b^2 - 4ac\) is negative in the quadratic formula?
2. How would the quadratic equation change if \(b = 0\)?
3. Can a quadratic equation have no real solutions? How would that happen?
4. What is the geometric interpretation of a quadratic equation's solution on a graph?
5. Can you solve a quadratic equation by factoring instead of using the quadratic formula?

**Tip:** The discriminant \(b^2 - 4ac\) determines the number and type of solutions: if it's positive, you get two real solutions; if it's zero, one real solution; and if it's negative, no real solutions (only complex).

Quadratic equation for 4x² - 4x + 1 = 0 using the following steps: 1. Determine the values of a, b, and c. 2. Substitute the values of a, b, and c in the quadratic formula. 3. Solve to find the solutions. 4. Application of the steps. 5. Check by substituting each solution in the original equation.

Learn how to solve the quadratic equation 4x² - 4x + 1 = 0 step by step using the quadratic formula. This tutorial covers algebraic concepts like identifying a, b, and c, solving for the discriminant, and checking solutions. Perfect for students in Grades 8-10.

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